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2 years ago

In a volleyball match Hanein serves the volleyball The height of the the ball above the court

Mathematics

1 answer:

forsale [732]2 years ago

7 0

(a) The maximum height of the ball above the ground is 12.5 m and the time of motion is 1.43 s.

(b) The time taken for the ball to contact the other player at 0.5 m above the ground is 3.0 s.

<h3>Maximum height reached by the ball</h3>

The maximum height reached by the ball is calculated as follows.

At maximum height, the final velocity, v = 0

dh/dt = v = 0

dh/dt = -2(4.9)t + 14

0 = -9.8t + 14

9.8t = 14

t = 1.43 s

H(1.43) = -4.9(1.43)² + 14(1.43) + 2.5

H(1.43) = -10.02 + 20.02 + 2.5

H(1.43) = 12.5 m

<h3>Time to reach maximum height</h3>

12.5 = -4.9t² + 14t + 2.5

4.9t² - 14t + 10 = 0

t = 1.43 s

<h3>Time for the ball to reach 0.5 m above the ground</h3>

0.5 = -4.9t² + 14t + 2.5

4.9t² - 14t + - 2 = 0

t = 3.0 seconds

The complete question is below:

In a volleyball match Hanein serves the volleyball at 14 m/s, from a height of 2.5 m above the court. The height of the ball in flight is estimated using the equation, h = -4.9t² + 14t + 2.5, where t is the time in second and h is height above ground, in metres.

Learn more about time of motion here: brainly.com/question/2364404

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About 16 % of the population of a large country is allergic to pollen. If two people are randomly selected, what is the probabil

Vinvika [58]

Answer:

(a) 0.0256

(b) 0.2944

Step-by-step explanation:

For solving this exercise we can apply the binomial distribution. The equation that give as the probability is:

$P(x,n,p)=(nCx)*p^{x} *(1-p)^{n-x}$

Where n is the number of identical events, p is the probability that the event has a success and x is the number of success in the n identical events.

Additionally, nCx is calculated as:

$nCx=\frac{n!}{x!(n-x)!}$

So, in this case we have 2 identical events because we are going to select two people randomly and the probability p of success is the probability that the person is allergic to pollen and this probability is 16%.

Then, for the first case, x is 2 because their are asking for the probability that both are allergic to pollen. Replacing the values of x, n and p we get:

$P(2,2,0.16)=(2C2)*0.16^{2} *(1-0.16)^{2-2}$

P(2,2,0.16)=0.0256

For the second case, their are asking for the probability that at least one is allergic to pollen, that means that we need to sum the probability that both are allergic to pollen with the probability that just one is allergic to pollen.

Using the same equation to calculate P(1,2,0.16) we get:

$P(1,2,0.16)=(2C1)*0.16^{1} *(1-0.16)^{2-1}$

P(1,2,0.16)=0.2688

So, the probability that at least one person is allergic to pollen is 0.2944 and it is calculated as:

0.0256 + 0.2688 = 0.2944

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3 years ago

Please help me i really need this grade !

Goshia [24]

Answer:

C. 8

Step-by-step explanation:

still using the equation a^2 = b^2 = c^2

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3 years ago

Proportions, assist me please!

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Step-by-step explanation:

$w = \frac{1}{2} {x}^{2} y \\ (2)w = \frac{1}{2} {x}^{2} y(2) \\ 2w = {x}^{2} y \\ \frac{2w}{ {x}^{2} } = \frac{{x}^{2} y}{ {x}^{2} } \\ \frac{2w}{ {x}^{2} } = y$